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Derivation of the kinetic wave equation


Date: Thursday, November 12, 2020 16:15 - 17:15
Speaker: Pierre Germain (CIMS, New York University)
Location: online via Zoom
Series: Mathematics and CS Seminar
Host: Laszlo Erdös

It is conjectured by physicists that, in the proper scaling, turbulent behavior in nonlinear dispersive equations can be modeled by kinetic models, similar to Boltzmann's equation arising from Newtonian dynamics. I will present results obtained with Charles Collot, which prove this conjecture up to the kinetic time scale less an arbitrarily small power. The proof relies on the analysis of Feynman graphs in the framework of Bourgain spaces, together with estimates on the distribution of sums of eigenvalues of the underlying linear problem.


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